This paper proposes a new approach to describe the dynamics of electric field strength in cumulonimbus clouds of mixed structure, taking into account the fractality of the cloud environment and its characteristic parameter of fractional structure. The model is based on the application of fractional integro-differentiation. It is shown that the fractality of cumulonimbus clouds, which have a fractal nature in time, directly affects the electrodynamic intra-cloud processes. Within the framework of the model, the fractal property of the cloud environment is taken into account through the phenomenological parameters \(\alpha (t)\) and \(\beta (t)\) , which determine the intensity of the electric field strength dynamics. The proposed approach is applicable to qualitatively complement the theory of thunderstorm electricity by considering the cloud as a natural object with a fractal structure.